Massimiliano Latorre made the appeal in an email to a journalist made public.
"Right now, it doesn't help us to know who to blame, because it doesn't lead us anywhere, and political parties bouncing responsibility off each other is even less useful," Latorre wrote to Mediaset reporter Toni Capuozzo.
"What we ask for now is not division, but that they link arms, join forces and resolve this tragedy", he was quoted by the Italian news agency ANSA.
Italian Foreign Minister Giulio Terzi resigned yesterday, protesting government's U-turn to send back the marines to India.
Tersi's decision to quit came four days after the Italian government reversed its earlier decision not to send back to India,
Latore and Salvatore Girone, who faced murder charges for shooting dead two Indian fishermen off Kerala coast in February last year.
Italy had first reneged on its assurance to Indian Supreme Court of sending back the two marines but later backtracked after both the Indian government and the apex court stepped up the heat amid New Delhi's warning of downgrading ties with Rome.
The Italian marines had flown back to New Delhi on March 22 after securing assurance from India that they will not face death penalty nor will they be arrested, bringing to an end the 11-day diplomatic row between the two countries.
As the diplomatic crisis escalated, India forbade Italian ambassador Daniele Mancini from leaving the country and airports were put on alert.
The dramatic U-turn by the Italian government, enabled the marines to meet the deadline set by the Supreme Court when it gave them permission to go for a month to vote in the elections here.
The two marines were serving as security guards on 'Enrica Lexie', an Italian oil tanker, when the incident occurred last year.